For example: Boston needs to travel to St. Louis to play a series, and that's a long distance to travel in 1880. Do they just send letters back and forth over the winter discussing possible dates? Or does the league just schedule all the games like they do today? Does the home team make arrangements for accommodations for the visiting team or does the team on the road make their own arrangements with local hotels by mail prior to arriving?
Before 1877, it was entirely up to the teams to schedule games themselves, the league itself had relatively no say in the matter. At this point in time, professional sports leagues weren’t really authoritative bodies, they were more like agreements between powerful clubs as to how they wanted the game to be played and how to determine who the best team was. The National Association, which was essentially the precursor to the National League from 1871-1875, mandated that each team play a certain amount of games against the others in order to be eligible for league champion, but had no authority to enforce this and it was entirely up to the teams to plan out when and where the games were to be played. This involved sending letters to each other or meeting in person whenever there was a league-wide meeting between representatives
Like you said, it was very expensive and time-consuming to travel halfway across the country for a baseball game, and every day travelling was a day not spent playing and a day spent not collecting ticket sales and concessions revenue. A team like Baltimore wouldn’t just take a train to Brooklyn, play a series, and then travel back south. Ticket sales were by far the largest source of income for teams, so ensuring a certain amount of home games was crucial to breaking even. To save time and money, teams would take long road trips to try and knock out all their required road games in two or three trips. It was the only way these teams could make ends meet while still playing the requisite games.
This would be nice and tidy if there were a constant amount of teams that could reliably be counted on to give every team an away team to play against. Unfortunately that wasn’t always the case. Oftentimes teams would schedule a road trip and not have enough money to recuperate the losses and fold. Sometimes teams would not gain the money they expected in home games early in the season and cancel a late season road trip. Since scheduling was up to the teams, there was no obligation for the league to enforce this schedule
By the time of the creation of the National League in 1876, pro baseball was becoming more entrenched in the midwest and the teams from the region were more financially stable and could be relied on to be intact by the end of the season, even if money was still tight. With more and more teams coming from the midwest, it became difficult to arrange month-long road trips without cooperation with other teams in the league. For example, if Boston travelled out west in 1876 they would need Cincinnati, Chicago, St. Louis, and Louisville to all be at home during that time. Remember, the rules of the league still stipulated that each team needed to play each other a certain amount of times at each other’s stadiums in order to be eligible to win the league, so every team had to travel to St Louis and Chicago eventually. What ended up happening was the east coast teams all went on road trips at the same time to knock out their road games against the midwest teams, and then the midwestern teams all went on road trips to known out their road games against the east coast teams, and then they repeated to get all the required games in.
However, the Philadelphia Athletics and the New York Mutuals didn’t like the financial prospects of traveling out west again, so they cancelled their games as would often happen in previous years. This rightfully pissed off the other owners in the NL. The National League was much more owner-controlled than other league organizations of the time, and the owners were able to expel them from the league. This brought an end to the independant team-centered scheduling system. For 1877 and beyond, the league created the schedule that the teams had to stick to or risk expulsion. Functionally it wasn’t all that different from the 1876 schedule, with month-long road trips to save costs and lessen overall travel distances, but it was one less thing the teams had to worry about doing themselves. It also must be noted that teams were free to play games outside the NL schedule as long as they played to their commitments of the league schedule. The NL was not the only professional league of the time, so there were a plethora of local teams present to call up at a moments notice to play, and extra home games meant more money. These exhibition games were entirely scheduled by the individual teams, and lasted well into the 20th century
In summary, up until 1877, it was up to the teams to make their own schedules, but it often required cooperation from several different teams in order to make it work. This partially involved writing letters to each other, but league meetings were also good ways to hash out schedules. 1877 was the first year the NL created its own schedule that teams were mandated to follow, but teams could still schedule games independently of the league.
For some reading into 19th century pro baseball, I highly recommend Warren Goldstein’s Playing for Keeps and The Great Encyclopedia of Nineteenth Century Major League Baseball by David Nemec, both are a little old but still great reads that do a pretty good job at capturing the culture surrounding the early days of the sport.